Matching van Stockum dust to Papapetrou vacuum
arXiv:2207.04740 · doi:10.1016/j.geomphys.2023.104878
Abstract
Addressing a long-standing problem, we show that every van Stockum dust can be matched to a 1-parametric family of non-static Papapetrou vacuum metrics, and the converse. The boundary, if existing, is determined by vanishing of certain first-order invariant on the vacuum side. Moreover, we establish a relation to Ehlers and Kramer--Neugebauer transformations, which allows us to look for dust clouds with a prescribed boundary. Explicit examples include the Bonnor metric and a new vacuum exterior to the Lanczos--van Stockum dust metric, as well as dust clouds with nontrivial topology.
13 pages, 1 figure. New in version 2: Sections 4, 8, 9, 10
References in corpus (5)
- Static axisymmetric rings in general relativity: How diverse they are
- van Stockum--Bonnor Spacetimes of Rigidly Rotating Dust
- The interior solution of axially symmetric, stationary and rigidly rotating dust configurations
- Just dust : About the (in)applicability of rotating dust solutions as realistic galaxy models
- Rigidly rotating dust solutions depending upon harmonic functions